I know it’s the old round pin we used for phones back in the day but can someone send me a link to the exact one because I’m seeing too many round pin charges of different sizes. Also where do I go for tech help related questions like these? Is this the right community?
Barrel plug, same as you'd find on the power supply for many laptops etc. You need to know:
the voltage/amps of the adaptor (may be listed on the bottom or side of the lamp). It must be the matching voltage, amps can be higher than listed
The barrel size (outer diameter, inner diameter, length), can be measured with calipers
Polarity of the tip
If there's an electronics repair place anywhere nearby they might be able to figure out the barrel size etc for you.
See also:
https://electronics.stackexchange.com/questions/33968/how-to-tell-polarity-expected-of-a-dc-barrel-jack